Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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GROUP OF POLYNOMIAL PERMUTATIONS OF ℤpr

  • Lee, Kwankyu (Department of Mathematics, Chosun University) ;
  • Lee, Heisook (Department of Mathematics, Ewha Womans University)
  • Received : 2012.07.23
  • Accepted : 2012.09.05
  • Published : 2012.12.25
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Abstract

The set of all polynomial permutations of $\mathbb{Z}_{p^r}$ forms a group. We investigate the structure of the group and some related groups, and completely determine the structure of the group of all polynomial permutations of $\mathbb{Z}_{p^2}$.

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References

  1. L. Carlitz, Functions and polynomials (mod $p^{n}$), Acta Arith. 9 (1964), 67-78. https://doi.org/10.4064/aa-9-1-67-78
  2. G. H. Hardy and E. M. Wright, An introduction to the theory of numbers, fourth edition, Oxford, 1960.
  3. G. Keller and F. R. Olson, Counting polynomial functions (mod $p^{n}$), Duke Math. Journal 35 (1968), 835-838. https://doi.org/10.1215/S0012-7094-68-03589-8
  4. R. Lidl and H. Niederreiter, Finite fields, Addison-Wesley, 1983.
  5. G. Mullen and H. Stevens, Polynomial functions (mod m), Acta Math. Hung. 44 (1984), no. 3-4, 237-241. https://doi.org/10.1007/BF01950276
  6. W. Nobauer, Uber gruppen von restklassen nach restpolynomidealen, Osterreich. Akad. Wiss. Math.-Nat. Kl. S.-B. IIa. 162 (1953), 207-233.
  7. R. L. Rivest, Permutation polynomials modulo $2^{\omega}$, Finite Fields Appl. 7 (2001), 287-292. https://doi.org/10.1006/ffta.2000.0282
  8. D. Singmaster, On polynomial functions (mod m), J. Number Theory 6 (1974), 345-352. https://doi.org/10.1016/0022-314X(74)90031-6